TRIANGLE CENTERS

Long before the first pencil and paper, some curious person drew a triangle in the sand and bisected the three angles. He noted that the bisectors met in a single point and decided to repeat the experiment on an extremely obtuse triangle. Again, the bisectors concurred. Astonished, the person drew yet a third triangle, and the same thing happened yet again!

Unlike squares and circles, triangles have many centers. The ancient Greeks found four: incenter, centroid, circumcenter, and orthocenter. A fifth center, found much later, is the Fermat point. Thereafter, points now called nine-point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added to the literature. In the 1980s, it was noticed that these special points share some general properties that now form the basis for a formal definition of
triangle center

The Encyclopedia of Triangle Centers
lists many centers, but without pictures. The purpose of this page is to introduce a collection of individual pictures, showing constructions of selected triangle centers. The selections are in two groups: Recent Triangle Centers and Classical Triangle Centers.